Air pipeline numerical modelling - how to take account of valves? 1

[bmorales]

Hi there

I´m modelling a air flow pipeline using Kirchoff laws and solving it through Newton method.

The trouble is when trying to add a valve in this system.

I´m programming myself this and cannot use any other software (besides the numerical recipes).

The system is composed of 4 fans and 4 elements which decrease pressure (

http://files.engineering.com/getfil...-b757-5b9309a8c0ee&file=exampleNetwork.jpeg).

The following assumptions hold:
- Steady-state
- Inlet and outlet pressures are equal to 1 atm (intake = discharge pressure)
- Pressure loss in pipes are negligible
- I know how to compute the pressure rise brought by fans and pressure decrease of the elements

Let Q be the flow rates, DP_Fan the pressure rise of fans, DP_el the pressure decrease of each element.

Applying 1st and 2nd Kirchoff laws, the following equations are obtained:

1st Law for node 1: Q1 + Q2 - Q3 = 0
1st Law for node 2: Q3 - Q4 - Q5 = 0
2nd Law for path 1/3: DP_Fan1 - DP_el1 - DP_el3 + DP_Fan3 = 0
2nd Law for path 1/4: DP_Fan1 - DP_el1 - DP_el4 + DP_Fan4 = 0
2nd Law for path 2/4: DP_Fan2 - DP_el2 - DP_el3 + DP_Fan3 = 0
2nd Law for path 2/4: DP_Fan2 - DP_el2 - DP_el4 + DP_Fan4 = 0

The first 2 equations may be rewritten as Q1 + Q2 - Q4 - Q5 = 0

The question is:

If a valve open to the atmosphere is placed between nodes 1 and 2, how shall I consider it in this analysis?

BTW: do any of you have read already Osiadacz book "Simulation and analysis of gas Networks"? Is it good?

Big thanks in advance.

 

[Latexman]

Try the Darcy-Weisbach equation.

Good luck,
Latexman

 

[bmorales]

Hi Latexman

Thanks for your kind help, but the focus of my doubt is not the pressure loss in the valve itself, but how the kirchoff equations will change with the valve addition.

Let´s assume that I know how to compute the pressure loss of a valve through Darcy-Weisbach.

Adding a valve to the system, how will the network analysis change?

Again, thanks for your help.

 

[BigInch]

Yes Osiadacz is an excellent text with lots of good examples, which by the way, you should read before you waste any more time. It's apparent you don't have a good understanding of hydraulic or network modeling just yet.

A valve open to atmosphere between nodes 1 and 2 would require that you break pipe 1-2 to add another node N3 there between N1 & N2, then the valve (new flow element Q = K * (P₃²-P₄²) connecting from N3 to a new N4, N4 representing a pressure contolled connection to atmosphere at 14.7 psia.

From "BigInch's Extremely simple theory of everything."

 

[bmorales]

Hi BigInch.

I appreciate your help.

I´m going follow your advice and study Osiadacz in order to get a clear understanding of the basics.

But I´d like to ask you for further help: you said that is apparent that my understanding on the subject is not enough.

Can you tell me if is there anything clearly wrong in the analysis of the original (without valve) network I shown above?

Thanks for your help.

 

[BigInch]

No. My comment was based only on seeing that apparently you didn't yet know to model a connection to atmos as another source/sink node with a constant pressure.

From "BigInch's Extremely simple theory of everything."

 

[bmorales]

Hello there again.

Do you know an alternative to Osiadacz's book?

I´m having a hard time find a copy of it.

Thanks in advance.

 

[BigInch]

Never seen an alternative.
Keep looking, it's worth it.

From "BigInch's Extremely simple theory of everything."

 

[Latexman]

Do a search on

http://www.addall.com.

It's available for US$40 to 140 plus shipping.

Good luck,
Latexman

 

[Latexman]

Ooops! Sorry, I looked at the wrong title. Amazon says "Simulation and analysis of gas Networks" is $140 to 240. 23 are available.

Good luck,
Latexman